Mathematical analysis of subwavelength resonant acoustic scattering in multi-layered high-contrast structures
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910906291585024 |
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| author | Deng, Youjun Kong, Lingzheng Liu, Yongjian Zhu, Liyan |
| author_facet | Deng, Youjun Kong, Lingzheng Liu, Yongjian Zhu, Liyan |
| contents | Multi-layered structures are widely used in the construction of metamaterial devices to realize various cutting-edge waveguide applications. This paper makes several contributions to the mathematical analysis of subwavelength resonances in a structure of $N$-layer nested resonators. Firstly, based on the Dirichlet-to-Neumann approach, we reduce the solution of the acoustic scattering problem to an $N$-dimensional linear system, and derive the optimal asymptotic characterization of subwavelength resonant frequencies in terms of the eigenvalues of an $N\times N$ tridiagonal matrix, which we refer to as the generalized capacitance matrix. Moreover, we provide a modal decomposition formula for the scattered field, as well as a monopole approximation for the far-field pattern of the acoustic wave scattered by the $N$-layer nested resonators. Finally, some numerical results are presented to corroborate the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05619 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mathematical analysis of subwavelength resonant acoustic scattering in multi-layered high-contrast structures Deng, Youjun Kong, Lingzheng Liu, Yongjian Zhu, Liyan Analysis of PDEs Multi-layered structures are widely used in the construction of metamaterial devices to realize various cutting-edge waveguide applications. This paper makes several contributions to the mathematical analysis of subwavelength resonances in a structure of $N$-layer nested resonators. Firstly, based on the Dirichlet-to-Neumann approach, we reduce the solution of the acoustic scattering problem to an $N$-dimensional linear system, and derive the optimal asymptotic characterization of subwavelength resonant frequencies in terms of the eigenvalues of an $N\times N$ tridiagonal matrix, which we refer to as the generalized capacitance matrix. Moreover, we provide a modal decomposition formula for the scattered field, as well as a monopole approximation for the far-field pattern of the acoustic wave scattered by the $N$-layer nested resonators. Finally, some numerical results are presented to corroborate the theoretical findings. |
| title | Mathematical analysis of subwavelength resonant acoustic scattering in multi-layered high-contrast structures |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.05619 |